# Neuro-Symbolic Financial Reasoning via Deterministic Fact Ledgers and Adversarial Low-Latency Hallucination Detector

arXiv: https://arxiv.org/abs/2603.04663 · HTML: https://mlsanity.com/paper/2603.04663/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 27 of its 34 references that are in the map.
- First posted on arXiv 4 Mar 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- Retrieval-augmented generation / [Legal and financial RAG](https://mlsanity.com/rag/legal-and-financial-rag/)

## Builds on (most cited first, 27 of 27)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [BEIR: A Heterogenous Benchmark for Zero-shot Evaluation of Information Retrieval Models](https://mlsanity.com/paper/2104.08663/) (2021)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Towards Understanding Sycophancy in Language Models](https://mlsanity.com/paper/2310.13548/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Red Teaming Language Models to Reduce Harms: Methods, Scaling Behaviors, and Lessons Learned](https://mlsanity.com/paper/2209.07858/) (2022)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Prometheus: Inducing Fine-grained Evaluation Capability in Language Models](https://mlsanity.com/paper/2310.08491/) (2023)
- [Textbooks Are All You Need](https://mlsanity.com/paper/2306.11644/) (2023)
- [FinQA: A Dataset of Numerical Reasoning over Financial Data](https://mlsanity.com/paper/2109.00122/) (2021)
- [TAT-QA: A Question Answering Benchmark on a Hybrid of Tabular and Textual Content in Finance](https://mlsanity.com/paper/2105.07624/) (2021)
- [HaluEval: A Large-Scale Hallucination Evaluation Benchmark for Large Language Models](https://mlsanity.com/paper/2305.11747/) (2023)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)
- [Make Your LLM Fully Utilize the Context](https://mlsanity.com/paper/2404.16811/) (2024)
- [Prompt Repetition Improves Non-Reasoning LLMs](https://mlsanity.com/paper/2512.14982/) (2025)
- [Greenback Bears and Fiscal Hawks: Finance is a Jungle and Text Embeddings Must Adapt](https://mlsanity.com/paper/2411.07142/) (2024)
- [FinLoRA: Benchmarking LoRA Methods for Fine-Tuning LLMs on Financial Datasets](https://mlsanity.com/paper/2505.19819/) (2025)
- [HalLoc: Token-level Localization of Hallucinations for Vision Language Models](https://mlsanity.com/paper/2506.10286/) (2025)
- [THOR: Tool-Integrated Hierarchical Optimization via RL for Mathematical Reasoning](https://mlsanity.com/paper/2509.13761/) (2025)
- [FRED: Financial Retrieval-Enhanced Detection and Editing of Hallucinations in Language Models](https://mlsanity.com/paper/2507.20930/) (2025)
- [Metadata-Driven Retrieval-Augmented Generation for Financial Question Answering](https://mlsanity.com/paper/2510.24402/) (2025)
- [SALSA: Single-pass Autoregressive LLM Structured Classification](https://mlsanity.com/paper/2510.22691/) (2025)

## Built on by (most cited first, 2 of 2)

- [FinVerBench: Benchmark Validity and Calibration in Large Language Model Financial Statement Verification](https://mlsanity.com/paper/2605.29586/) (2026)
- [Memory-Orchestrated Semantic System (MOSS): An Auditable Agentic Memory Architecture](https://mlsanity.com/paper/2607.04391/) (2026)

## Abstract (arXiv)

Standard Retrieval-Augmented Generation (RAG) architectures fail in high-stakes financial domains due to two fundamental limitations: the inherent arithmetic incompetence of Large Language Models (LLMs) and the distributional semantic conflation of dense vector retrieval (e.g., mapping "Net Income" to "Net Sales" due to contextual proximity). In deterministic domains, a 99% accuracy rate yields 0% operational trust. To achieve zero-hallucination financial reasoning, we introduce the Verifiable Numerical Reasoning Agent (VeNRA). VeNRA shifts the RAG paradigm from retrieving probabilistic text to retrieving deterministic variables via a strictly typed Universal Fact Ledger (UFL). We mathematically bound this ledger using a novel Double-Lock Grounding algorithm. Coupled with deterministic Python execution, this neuro-symbolic routing compresses systemic hallucination rates to a near-zero 1.2%. Recognising that upstream parsing anomalies inevitably occur, we introduce the VeNRA Sentinel: a 3-billion parameter SLM trained to forensically audit candidate using a single-token inference budget with optional post-hoc reasoning. To train the Sentinel, we steer away from traditional hallucination datasets in favour of Adversarial Simulation, programmatically sabotaging financial records to simulate Ecological Errors. The compact Sentinel consequently outperforms 70B+ frontier models in error detection. Through Loss Dilution phenomenon in Reverse-CoT training, we present a novel Micro-Chunking loss algorithm to stabilise gradients under extreme verdict penalisation, yielding a 28x latency speedup without sacrificing forensic rigor.